Imaging the He ₂ quantum halo state using a free electron laser

Abstract

Quantum tunneling is a ubiquitous phenomenon in nature and crucial for many technological applications. It allows quantum particles to reach regions in space which are energetically not accessible according to classical mechanics. In this "tunneling region," the particle density is known to decay exponentially. This behavior is universal across all energy scales from nuclear physics to chemistry and solid state systems. Although typically only a small fraction of a particle wavefunction extends into the tunneling region, we present here an extreme quantum system: a gigantic molecule consisting of two helium atoms, with an 80% probability that its two nuclei will be found in this classical forbidden region. This circumstance allows us to directly image the exponentially decaying density of a tunneling particle, which we achieved for over two orders of magnitude. Imaging a tunneling particle shows one of the few features of our world that is truly universal: the probability to find one of the constituents of bound matter far away is never zero but decreases exponentially. The results were obtained by Coulomb explosion imaging using a free electron laser and furthermore yielded He 2 's binding energy of 151.9 ± 13.3 neV, which is in agreement with most recent calculations.clusters | helium dimer | wavefunction | tunneling A ttractive forces allow particles to condense into stable bound systems such as molecules or nuclei with a ground state and (in most cases) energetically excited bound states, as shown in Fig. 1. Classical particles situated in such a binding potential oscillate back and forth between two turning points. The regions beyond these points are inaccessible for a classical particle due to a lack of energy. Quantum particles, however, can penetrate into the potential barrier by a phenomenon known as "tunneling." Tunneling is omnipresent in nature and occurs on all energy scales from megaelectron volts in nuclear physics to electron volts in molecules and solids and to nanoelectron volts in optical lattices. For bound matter, the fraction of the probability density distribution in this classically forbidden region is usually small. For shallow short-range potentials, this situation can change dramatically: upon decreasing the potential depth, excited states are expelled one after the other as they become unbound (transition from A to B in Fig. 1). A further decrease of the potential depth effects the ground state as well, as more and more of its wavefunction expands into the tunneling region ( Fig. 1 C and D). Consequently, at the threshold (i.e., in the limit of vanishing binding energy), the size of the quantum system expands to infinity. For short-range potentials, this expansion is accompanied by the fact that the system becomes less "classical" and more quantumlike. Systems existing near that threshold (and therefore being dominated by the tunneling part of their wavefunction) are called "quantum halo states" (1). These states are known, for example, from nuclear physics where 11 Be and 11 Li form ...

Pair Potential with Submillikelvin Uncertainties and Nonadiabatic Treatment of the Halo State of the Helium Dimer

“…rived from a nanosieve transmission experiment [13]. The value D 0 =151.9±13.3 neV, obtained very recently [14] using the Coulomb explosion technique, agrees with our theoretical prediction within 0.98 σ.…”

“…The dimer composed of 4 He atoms, 4 He 2 , has a single very weakly bound vibrational state-an example of a quantum halo state-where atoms move mainly in the classically forbidden tunneling region of the configuration space [8]. This state was the subject of several experimental investigations [9][10][11][12][13][14]. We present here the development of a new potential with uncertainties reduced by an order of magnitude compared to the previous most accurate determination [15].…”

“…Recently, the wave function of 4 He 2 has been measured via the Coulomb explosion technique [14], which enabled the first experimental determination of its very small binding energy (151.9±13.3 neV). The most precise calculation for this state was performed [15] in the adiabatic approximation giving the binding energy D 0 =136.6±2.9 neV when nuclear masses are used to solve the vibrational problem (as required by the mathematical derivation of the adiabatic approximation) or 139.2±2.9 neV when the atomic masses are used (as suggested by physical intuition).…”

The Linac Coherent Light Source: Recent Developments and Future Plans

“…Here specific molecular dynamics are initiated via tailored transient excitations, such as charge transfer, vibrational excitation, the creation of a valence hole via ionization, or the creation of non-equilibrium Rydberg wavepackets. Recent experiments highlight the promising opportunities for dynamic reaction microscope studies at high repetition rate XFELs [34][35][36][37]. For example, LCLS experiments at 120 Hz by Erk et al on charge-transfer processes in gas-phase iodomethane [33] identified three dissociative channels based on the time-dependent kinetic energy distributions of the charged fragments (Figure 9 right).…”

Dimensional Effects in Efimov Physics

“…A direct measurement of the Efimov trimer energies and also the heliumdimer wave function [11] shows that a new aspect in few-body physics would be interesting to be studied in experiments: how the effective spatial dimension in atomic traps influence the observables related to Efimov physics. The question of dimensionality is frequently explored in the context of many atoms.…”